Split Pea Soup With Ham

I found the start of this recipe on AllRecipes.com submitted by Chef John who has a great site called FoodWishes.com. I made it a few times following the recipe exactly. I then saw a recipe on CooksIllustrated.com and saw they had a variation with the addition of caraway seed (which I'm crazy for). The result is the recipe linked below. I'm toying with the idea of substituting ham hock for the ham steak, but the ease of dicing the ham gives me pause. 

Ingredients

• 2 tablespoons butter
• 1 large onion, chopped medium
• 2 ribs celery, chopped medium
• 2 medium carrots, chopped medium
• 2 cloves garlic, sliced
• 1 pound ham steak, diced into 1/4 inch cubes
• 2 whole bay leaves, broken in 1/2
• 1 1/2 teaspoon caraway seed
• 1 pound dried split peas, picked over
• 1 quart chicken stock, low sodium
• 2 1/2 cups water
• salt and ground black pepper, to taste

Directions

1. Place the butter in a large soup pot over medium-low heat. Stir in onion, celery, and carrot with some salt. SLOWLY cook the vegetables so as not to brown. Add sliced garlic after 2 minutes. Cook slowly until the onions are translucent but not brown, About 5 to 8 minutes.
2. While vegetables are cooking, toast caraway seeds in small skillet over medium-high heat, stirring frequently, until fragrant and browned, about 4 minutes.
3. Mix in ham, bay leaf, caraway, and split peas. Pour in chicken stock and water. Stir to combine, and simmer slowly until the peas are tender and the soup is thick, about 1 hour and 15 minutes. Stir occasionally. Add more liquid if soup becomes too thick. Season with salt and pepper to taste (probably will not need any salt). Remove the 4 bay leaf pieces. 
4. Add a few grinds of black pepper about 5 min before you serve.
5. Serve with oyster crackers or caraway rye bread toasted.